Chapter 5 - Inner Product Spaces - 5.3 The Gram-Schmidt Process - True-False Review - Page 365: c

False

Let $x_1,x_2,x_3$ be linearly independent vectors in an inner product space $V$ Apply Gram-Schmidt process to the set $\{x_1,x_2,x_3\}$ gives $v_1=x_1$ Apply Gram-Schmidt process to the set $\{x_3,x_2,x_1\}$ gives $v_1'=x_3$ Since $x_1 \ne x_3$, the ordered orthogonal bases obtained by applying the Gram-Schmidt process to the set $\{x_1,x_2,x_3\}$ and $\{x_3,x_2,x_1\}$ are distinct.